Well, this is a new topic for me. So forgive any errors in advance. Here's my archair quarterback thoughts:
1. Cooling intake air means denser charge = more power.
2. Methanol is a fuel, so it ofsets the additional air with the extra fuel = not going lean.
3. Cooler charge means more timing advance = more power
4. Methanol is NOT as high pressure as Nitrous, so it's safer to run 100% of the time, which can't be run 100% (even if it were legal).

That was the basis for my question. Realistically, I would guess running methanol would give maybe 20 HP, which is really just the HP lost due to heat soak combined with a few extra from the extra air and Fuel. But I figured "why not" and opened up the question to the group.

ok, lets get some basics out of the way:

Methanol, the fuel, has an extremely high octane rating, so the racers use it in high compression engines to control pre-ignition. the drawback is its energy density is alot lower than gasoline, so you have to run 3 to 4 times as much fuel to produce the same power..

Nitrous Oxide is an oxydizer. nothing more. you want more power, you must have more oxygen to oxidize, or burn, the fuel. Nitrous dumps a ton of oxygen into the intake air, leaning it out, so you must add more fuel.. usually a bump injector..

a bi-product of methanol is an extremely low boiling point, so the forced induction crowd would inject a small amount into the charge air to absorb some heat & cool the intake charge down.. You could do the same with water, but it would take two to three times as much water to remove the same amount of heat from the charge temp...

more power requires more oxygen, or air. this is the supreme fundamental to creating more power. the more air, the more fuel you can burn. this is the basis for the saying: